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Info to Readers click to show or hide Mathesis Universalis: It is never quite clear what the modern concept of mathesis universalis as such exactly signifies, let alone how it may be defined.
Hence the first and general sense of mathesis universalis signifies no more than universal science disciplina universalis or scientia universalis.
However — and this will be very important — since this "science" has a rather mathematical ring to it, we should on second thoughts take it to be an equivalent of s cientia mathematica universalis 3 or generalis or communis: This more specific meaning, i.
However, the emphasis of this paper lies, with regard to the concept of mathesis universalis not so much on the historical details as on the more general systematical outlines. Therefore it should suffice to begin our work with an understanding of mathesis universalis that implies not much more than universal or general or common mathematical science, which of course still allows for a range of diverse meanings.
What matters is to remain true to the sense of mathesis universalis while not confusing the two very different notions somehow inherent in the Latin, i. A clear line should be drawn between these two concepts, of which the former is mathematical even though sometimes in a wider sensethe latter not.
I trust that it will become clear in this paper that both for historical and systematical reasons it is not only justified, but even necessary, to draw this general distinction between universal mathematic and universal science in this way. For the history of the term as such cf. Kauppi, "Mathesis universalis", in: Neues Jahrbuch 4 Gerald Bechtle, "How to apply the modern concepts of Mathesis Universalis and Scientia Universalis to ancient philosophy.
Aristotle, Platonisms, Gilbert of Poitiers, and Descartes". Ancient, Modern, and Postmodern. However, the significance of MU is not restricted to that period. It belongs to main ideas of Western civilization, its beginnings can be traced to Pythagoreans and Plato. Immediate sources of the 17th century MU are found in the 15th century revival of Platonism whose leading figure was Marsilio Ficinothe author of "Theologia Platonica".
He was accompanied by Nicholas of CusaLeonardo da Vincialso by Nicolaus Copernicus All of them may have taken as their motto the biblic verse, willingly quoted by St.
Augustine, Omnia in numero et pondere et mensura disposuisti, Sap. This line of thought was continued in the 16th century by Galileo Galilei and Johannes Kepler ; it penetrated not only mechanics and astronomy but also medical sciences as represented by Teophrastus Paracelsus of Salzburg No wonder that in the 17th century the community of scholars was ready to treat the idea of MU as something obvious, fairly a commonplace, before Descartes made use of this term in his "Regulae ad directionem ingenii".
Arndt, Hildesheim, Georg Olms, The last of the listed titles involves one of the key concepts of the MU program: There were two approaches to this art, differing from each other by opposite evaluations of formal logic.
According to Descartes, formal logic of Aristotle and schoolmen was useless for the discovery of truth; according to Leibniz, ars inveniendi was to possess the essential feature both of formal logic and of mathematical calculus, viz. Witold Marciszewski,"The principle of comprehension as a present-day contribution to mathesis universalis," Philosophia Naturalis According to Husserl, Leibniz saw the possibility of combining the formalized scholastic logic with other formal disciplines devoted to the forms that governed, for example, quantity or spatial relations or magnitude.
Leibniz distinguished between a narrower and a broader sense of mathesis universalis.
In the narrower sense, it is the algebra of our ordinary understanding, the formal science of quantities. But since the formalization at work in algebra already makes conceivable a purely formal mathematical analysis that abstracts from the materially determinate mathematical disciplines such as geometry, mechanics, and acoustics, we arrive at a broader concept emptied of all material content, even that of quantity.
When applied to judgments, this formal discipline yields a syllogistic algebra or mathematical logic. But, according to Leibniz, this formal analysis of judgment ought to be combinable with all other formal analyses.
Hence, the broader mathesis universalis would identify the forms of combination applicable in any science, whether quantitative or qualitative. Only thereby would it achieve the formality allowing it to serve as the theory-form for any science, whatever the material region to which that science is directed.
According to Husserl, however, Leibniz does not give an adequate account of how this unity is achieved. Moreover, when the principles of a mathematical logic are applied to any object whatever, it becomes clear, given the identity of the judgment as posited and the judgments as supposed, that mathematical logic can also be understood as formal ontology.
Formal ontology as the formal theory of objects is characterized in the first instance by its contrast with formal apophantic logic. These categories include object, state of affairs, unity, plurality, number, relation, set, ordered set, combination, connection, and the like.Angles and Directions The most common relative directions are left, right, forward(s), backward(s), up, and down.
x y z Angles and Directions In planar geometry, an angle is the figure formed. Poeta Calculans: Harsdorffer, Leibniz, and the Mathesis Universalis.
Jan C. Westerhoff - - Journal of the History of Ideas 60 (3) La «mathématique universelle» entre mathématique et philosophie, d'Aristote à Proclus.
Other articles where Mathesis Universalis is discussed: John Wallis: In Wallis published the Mathesis Universalis (“Universal Mathematics”), on algebra, arithmetic, and geometry, in which he further developed notation. He invented and introduced the symbol ∞ for infinity.
Mathesis universalis (Greek μάθησις, mathesis "science or learning", Latin universalis "universal") is a hypothetical universal science modeled on mathematics envisaged by Descartes and Leibniz, among a number of more minor 16th and 17th century philosophers and mathematicians.
Universal language may refer to a hypothetical or historical language spoken and understood by all or most of the world's population.
In some contexts, it refers to a means of communication said to be understood by all living things, beings, and objects alike. "To grant me a vision of Nature's forces that bind the world, all its seeds and sources and innermost life all this I shall see and stop peddling in words that mean nothing to me.".